.file "tanf.s" // Copyright (c) 2000, Intel Corporation // All rights reserved. // // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, // and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. // // WARRANTY DISCLAIMER // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // // Intel Corporation is the author of this code, and requests that all // problem reports or change requests be submitted to it directly at // http://developer.intel.com/opensource. // // History //============================================================== // 2/02/00: Initial version // 4/04/00 Unwind support added // // API //============================================================== // float tanf( float x); // // Overview of operation //============================================================== // If the input value in radians is |x| >= 1.xxxxx 2^10 call the // older slower version. // // The new algorithm is used when |x| <= 1.xxxxx 2^9. // // Represent the input X as Nfloat * pi/2 + r // where r can be negative and |r| <= pi/4 // // tan_W = x * 2/pi // Nfloat = round_int(tan_W) // // tan_r = x - Nfloat * (pi/2)_hi // tan_r = tan_r - Nfloat * (pi/2)_lo // // We have two paths: p8, when Nfloat is even and p9. when Nfloat is odd. // p8: tan(X) = tan(r) // p9: tan(X) = -cot(r) // // Each is evaluated as a series. The p9 path requires 1/r. // // The coefficients used in the series are stored in a table as // are the pi constants. // // Registers used //============================================================== // // predicate registers used: // p6, p7, p8, p9, p10 // // floating-point registers used: // f32 -> f93 // f8, input // // general registers used // r32 -> r43 // // Assembly macros //============================================================== tan_Inv_Pi_by_2 = f32 tan_Pi_by_2_hi = f33 tan_Pi_by_2_lo = f34 tan_P0 = f35 tan_P1 = f36 tan_P2 = f37 tan_P3 = f38 tan_P4 = f39 tan_P5 = f40 tan_P6 = f41 tan_P7 = f42 tan_P8 = f43 tan_P9 = f44 tan_P10 = f45 tan_P11 = f46 tan_P12 = f47 tan_P13 = f48 tan_P14 = f49 tan_P15 = f50 tan_Q0 = f51 tan_Q1 = f52 tan_Q2 = f53 tan_Q3 = f54 tan_Q4 = f55 tan_Q5 = f56 tan_Q6 = f57 tan_Q7 = f58 tan_Q8 = f59 tan_Q9 = f60 tan_Q10 = f61 tan_r = f62 tan_rsq = f63 tan_rcube = f64 tan_v18 = f65 tan_v16 = f66 tan_v17 = f67 tan_v12 = f68 tan_v13 = f69 tan_v7 = f70 tan_v8 = f71 tan_v4 = f72 tan_v5 = f73 tan_v15 = f74 tan_v11 = f75 tan_v14 = f76 tan_v3 = f77 tan_v6 = f78 tan_v10 = f79 tan_v2 = f80 tan_v9 = f81 tan_v1 = f82 tan_int_Nfloat = f83 tan_Nfloat = f84 tan_NORM_f8 = f85 tan_W = f86 tan_y0 = f87 tan_d = f88 tan_y1 = f89 tan_dsq = f90 tan_y2 = f91 tan_d4 = f92 tan_inv_r = f93 ///////////////////////////////////////////////////////////// tan_AD = r33 tan_GR_10009 = r34 tan_GR_17_ones = r35 tan_GR_N_odd_even = r36 tan_GR_N = r37 tan_signexp = r38 tan_exp = r39 tan_ADQ = r40 GR_SAVE_B0 = r42 GR_SAVE_PFS = r41 GR_SAVE_GP = r43 .data .align 16 double_tan_constants: data8 0xA2F9836E4E44152A, 0x00003FFE // 2/pi data8 0xC90FDAA22168C234, 0x00003FFF // pi/2 hi data8 0xBEEA54580DDEA0E1 // P14 data8 0x3ED3021ACE749A59 // P15 data8 0xBEF312BD91DC8DA1 // P12 data8 0x3EFAE9AFC14C5119 // P13 data8 0x3F2F342BF411E769 // P8 data8 0x3F1A60FC9F3B0227 // P9 data8 0x3EFF246E78E5E45B // P10 data8 0x3F01D9D2E782875C // P11 data8 0x3F8226E34C4499B6 // P4 data8 0x3F6D6D3F12C236AC // P5 data8 0x3F57DA1146DCFD8B // P6 data8 0x3F43576410FE3D75 // P7 data8 0x3FD5555555555555 // P0 data8 0x3FC11111111111C2 // P1 data8 0x3FABA1BA1BA0E850 // P2 data8 0x3F9664F4886725A7 // P3 double_Q_tan_constants: data8 0xC4C6628B80DC1CD1, 0x00003FBF // pi/2 lo data8 0x3E223A73BA576E48 // Q8 data8 0x3DF54AD8D1F2CA43 // Q9 data8 0x3EF66A8EE529A6AA // Q4 data8 0x3EC2281050410EE6 // Q5 data8 0x3E8D6BB992CC3CF5 // Q6 data8 0x3E57F88DE34832E4 // Q7 data8 0x3FD5555555555555 // Q0 data8 0x3F96C16C16C16DB8 // Q1 data8 0x3F61566ABBFFB489 // Q2 data8 0x3F2BBD77945C1733 // Q3 data8 0x3D927FB33E2B0E04 // Q10 .align 32 .global tan# //////////////////////////////////////////////////////// .section .text .global tanf .proc tanf .align 32 tanf: // The initial fnorm will take any unmasked faults and // normalize any single/double unorms { .mmi alloc r32=ar.pfs,1,11,0,0 (p0) addl tan_AD = @ltoff(double_tan_constants), gp nop.i 999 } ;; { .mmi ld8 tan_AD = [tan_AD] nop.m 999 nop.i 999 } ;; { .mfi nop.m 999 (p0) fnorm tan_NORM_f8 = f8 (p0) mov tan_GR_17_ones = 0x1ffff ;; } { .mfi nop.m 999 nop.f 999 (p0) mov tan_GR_10009 = 0x10009 ;; } { .mmi adds tan_ADQ = double_Q_tan_constants - double_tan_constants, tan_AD (p0) ldfe tan_Inv_Pi_by_2 = [tan_AD],16 nop.i 999 } ;; { .mfi (p0) ldfe tan_Pi_by_2_hi = [tan_AD],16 (p0) fclass.m.unc p6,p0 = f8, 0x07 } { .mfi (p0) ldfe tan_Pi_by_2_lo = [tan_ADQ],16 nop.f 999 nop.i 999 ;; } { .mmb (p0) ldfd tan_P14 = [tan_AD],8 (p0) ldfd tan_Q8 = [tan_ADQ],8 nop.b 999 ;; } { .mmb (p0) ldfd tan_P15 = [tan_AD],8 (p0) ldfd tan_Q9 = [tan_ADQ],8 nop.b 999 ;; } { .mmb (p0) ldfd tan_P12 = [tan_AD],8 (p0) ldfd tan_Q4 = [tan_ADQ],8 nop.b 999 ;; } { .mmb (p0) ldfd tan_P13 = [tan_AD],8 (p0) ldfd tan_Q5 = [tan_ADQ],8 nop.b 999 ;; } { .mmb (p0) ldfd tan_P8 = [tan_AD],8 (p0) getf.exp tan_signexp = tan_NORM_f8 nop.b 999 ;; } { .mmb (p0) ldfd tan_P9 = [tan_AD],8 (p0) ldfd tan_Q6 = [tan_ADQ],8 (p6) br.ret.spnt b0 ;; } { .mmi (p0) ldfd tan_P10 = [tan_AD],8 (p0) ldfd tan_Q7 = [tan_ADQ],8 (p0) and tan_exp = tan_GR_17_ones, tan_signexp ;; } // p7 is true if we must call DBX TAN // p7 is true if f8 exp is > 0x10009 (which includes all ones // NAN or inf) { .mfi (p0) ldfd tan_P11 = [tan_AD],8 (p0) fma.s1 tan_W = tan_NORM_f8, tan_Inv_Pi_by_2, f0 (p0) cmp.ge.unc p7,p0 = tan_exp,tan_GR_10009 } { .mfi (p0) ldfd tan_Q0 = [tan_ADQ],8 nop.f 999 nop.i 999 ;; } { .mmb (p0) ldfd tan_P4 = [tan_AD],8 (p0) ldfd tan_Q1 = [tan_ADQ],8 (p7) br.cond.spnt TAN_DBX ;; } { .mmb (p0) ldfd tan_P5 = [tan_AD],8 (p0) ldfd tan_Q2 = [tan_ADQ],8 nop.b 999 ;; } { .mmb (p0) ldfd tan_P6 = [tan_AD],8 (p0) ldfd tan_Q3 = [tan_ADQ],8 nop.b 999 ;; } { .mmi (p0) ldfd tan_P7 = [tan_AD],8 (p0) ldfd tan_Q10 = [tan_ADQ],8 nop.i 999 ;; } // tan_int_Nfloat = Round_Int_Nearest(tan_W) { .mfi (p0) ldfd tan_P0 = [tan_AD],8 (p0) fcvt.fx.s1 tan_int_Nfloat = tan_W nop.i 999 ;; } { .mmi (p0) ldfd tan_P1 = [tan_AD],8 nop.m 999 nop.i 999 ;; } { .mfi (p0) ldfd tan_P2 = [tan_AD],8 nop.f 999 nop.i 999 ;; } { .mmi (p0) ldfd tan_P3 = [tan_AD],8 nop.m 999 nop.i 999 ;; } { .mfi nop.m 999 (p0) fcvt.xf tan_Nfloat = tan_int_Nfloat nop.i 999 ;; } { .mmi nop.m 999 (p0) getf.sig tan_GR_N = tan_int_Nfloat nop.i 999 ;; } { .mmi nop.m 999 nop.m 999 (p0) and tan_GR_N_odd_even = 0x1, tan_GR_N ;; } // p8 ==> even // p9 ==> odd { .mmi nop.m 999 nop.m 999 (p0) cmp.eq.unc p8,p9 = tan_GR_N_odd_even, r0 ;; } // tan_r = -tan_Nfloat * tan_Pi_by_2_hi + x { .mfi nop.m 999 (p0) fnma.s1 tan_r = tan_Nfloat, tan_Pi_by_2_hi, tan_NORM_f8 nop.i 999 ;; } // tan_r = tan_r -tan_Nfloat * tan_Pi_by_2_lo { .mfi nop.m 999 (p0) fnma.s1 tan_r = tan_Nfloat, tan_Pi_by_2_lo, tan_r nop.i 999 ;; } { .mfi nop.m 999 (p0) fma.s1 tan_rsq = tan_r, tan_r, f0 nop.i 999 ;; } { .mfi nop.m 999 (p9) frcpa.s1 tan_y0, p10 = f1,tan_r nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v18 = tan_rsq, tan_P15, tan_P14 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v4 = tan_rsq, tan_P1, tan_P0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v16 = tan_rsq, tan_P13, tan_P12 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v17 = tan_rsq, tan_rsq, f0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v12 = tan_rsq, tan_P9, tan_P8 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v13 = tan_rsq, tan_P11, tan_P10 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v7 = tan_rsq, tan_P5, tan_P4 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v8 = tan_rsq, tan_P7, tan_P6 nop.i 999 ;; } { .mfi nop.m 999 (p9) fnma.s1 tan_d = tan_r, tan_y0, f1 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v5 = tan_rsq, tan_P3, tan_P2 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_v11 = tan_rsq, tan_Q9, tan_Q8 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v12 = tan_rsq, tan_rsq, f0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v15 = tan_v17, tan_v18, tan_v16 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v7 = tan_rsq, tan_Q5, tan_Q4 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v11 = tan_v17, tan_v13, tan_v12 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v14 = tan_v17, tan_v17, f0 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_v8 = tan_rsq, tan_Q7, tan_Q6 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v3 = tan_rsq, tan_Q1, tan_Q0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v3 = tan_v17, tan_v5, tan_v4 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v6 = tan_v17, tan_v8, tan_v7 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_y1 = tan_y0, tan_d, tan_y0 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v10 = tan_v12, tan_Q10, tan_v11 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_dsq = tan_d, tan_d, f0 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v9 = tan_v12, tan_v12,f0 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_v4 = tan_rsq, tan_Q3, tan_Q2 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v6 = tan_v12, tan_v8, tan_v7 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v10 = tan_v14, tan_v15, tan_v11 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_y2 = tan_y1, tan_d, tan_y0 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_d4 = tan_dsq, tan_dsq, tan_d nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v2 = tan_v14, tan_v6, tan_v3 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_v9 = tan_v14, tan_v14, f0 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_v2 = tan_v12, tan_v4, tan_v3 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v5 = tan_v9, tan_v10, tan_v6 nop.i 999 ;; } { .mfi nop.m 999 (p9) fma.s1 tan_inv_r = tan_d4, tan_y2, tan_y0 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 tan_rcube = tan_rsq, tan_r, f0 nop.i 999 ;; } { .mfi nop.m 999 (p8) fma.s1 tan_v1 = tan_v9, tan_v10, tan_v2 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 tan_v1 = tan_v9, tan_v5, tan_v2 nop.i 999 ;; } { .mfb nop.m 999 (p8) fma.s f8 = tan_v1, tan_rcube, tan_r (p0) nop.b 999 } { .mfb nop.m 999 (p9) fms.s.s0 f8 = tan_r, tan_v1, tan_inv_r (p0) br.ret.sptk b0 ;; } .endp tanf .proc TAN_DBX TAN_DBX: .prologue { .mfi nop.m 0 nop.f 0 .save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs // Save ar.pfs };; { .mfi mov GR_SAVE_GP=gp // Save gp nop.f 0 .save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 // Save b0 } .body { .mfi nop.m 999 (p0) fmerge.s f9 = f1,f1 nop.i 999 ;; } { .mib nop.m 999 nop.i 999 (p0) br.call.sptk.many b0=__libm_tan# ;; } { .mmi mov gp = GR_SAVE_GP // Restore gp nop.m 999 mov b0 = GR_SAVE_B0;; // Restore return address } { .mfi nop.m 999 (p0) fnorm.s f8 = f8 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs };; { .mib nop.m 999 nop.i 999 (p0) br.ret.sptk b0 ;; } .endp TAN_DBX .type __libm_tan#,@function .global __libm_tan#